The present invention relates to the application of move-out correction to seismic data.
Seismic data are typically gathered using an array of detectors. In the case of marine data, hydrophones measure pressure fluctuations in the water caused by incoming seismic waves. Geophones measure vector quantities such as displacement, velocity or acceleration. In the case of marine data, a plurality of cables or streamers, which are spaced apart typically by about 100 meters, are towed behind a boat. Each cable has detectors spaced along the cable at intervals. In the case of land data, a geophone array is laid out on the ground with the geophones in an approximate grid formation. The detector array detects seismic signals from reverberations of a signal from a seismic source, such as an airgun for marine data. In Ocean Bottom (OBC or OBS) acquisition, a detector array is fixed on the sea bed. The source may be an airgun mounted on a boat.
The distance between a seismic source and a receiver is known as the offset. A flat reflector will generate an event of an approximately hyperbolic form as a function of offset. Move-out correction can be viewed as a process that compensates for offset by distorting the traces along the time axis in a manner that depends on a velocity function. The aim may be to simulate zero offset data and thus “flatten” the hyperbolic event, using a velocity function selected to match the velocity of the seismic energy through the water and the earth. This may be because the algorithm involves a zero offset assumption, in which case an accurate velocity function is desirable. One example of a data processing algorithm of this type is migration. However, very often move-out correction is applied preceding another data processing algorithm, typically to reduce aliasing effects. If the purpose is simply to reduce the slope of the hyperbolic events to avoid aliasing, an accurate velocity function is not required. In this case, the data are often purposely under corrected using a velocity function faster than one which would create zero offset data. After the data processing algorithm is applied, the move-out correction is reversed or “backed off”. One example of a type of data processing algorithm in which move-out correction is used in this way is interpolation.
Recent developments in marine acquisition record not only the pressure using hydrophones but also record particle velocity or acceleration in directions parallel to the surface. This allows the gathering of pressure gradient (or spatial derivative) data, in addition to pressure data. New algorithms are being developed which utilize both pressure data and pressure gradient data. However, if move-out correction is required it is not correct simply to apply move-out correction to the gradient, because this does not yield the derivative of the move-out-corrected data. Move-out-correction and differentiation do not, in general, commute.